This paper contains estimates for the effective reproduction number \(R_{t,m}\) over time \(t\) in various countries \(m\) of the world. This is done using the methodology as described in [1]. These have been implemented in R using EpiEstim package [2] which is what is used here. The methodolgy and assumptions are described in more detail here.
This paper and it’s results should be updated roughly daily and is available online.
As this paper is updated over time this section will summarise significant changes. The code producing this paper is tracked using Git. The Git commit hash for this project at the time of generating this paper was 2f23b49bb3138389fe9999536f79069c223283c5.
Data are downloaded from [3]. Minor formatting is applied to get the data ready for further processing.
Below we plot cumulative case count on a log scale by continent. Note that “Other” relates to ships.
Reported Cases by Continent
Below we plot the cumulative deaths by country on a log scale:
Reported Deaths by Continent
The methodology is described in detail here. We filter out countries with populations of greater than 500 000. Weeks where the deaths or cases are not greater than 50 are left out of results.
Below current (last weekly) \(R_{t,m}\) estimates are plotted on a world map.
Below we show various extremes of \(R_{t,m}\) where counts (deaths or cases) exceed 50 in the last week.
| Country | Estimated Type | Count (Last Week) | Week Ending | R - Lower CI | R - Mean | R - Uppper CI |
|---|---|---|---|---|---|---|
| Guatemala | deaths | 74 | 2020-11-28 | 0.4 | 0.5 | 0.7 |
| Sweden | deaths | 115 | 2020-11-28 | 0.5 | 0.6 | 0.7 |
| Pakistan | deaths | 339 | 2020-11-28 | 0.6 | 0.7 | 0.8 |
| Belgium | deaths | 746 | 2020-11-28 | 0.7 | 0.7 | 0.8 |
| Philippines | deaths | 230 | 2020-11-28 | 0.7 | 0.8 | 0.9 |
| Bolivia | deaths | 54 | 2020-11-28 | 0.6 | 0.8 | 1.1 |
| Kenya | deaths | 92 | 2020-11-28 | 0.7 | 0.8 | 1.0 |
| Bosnia_and_Herzegovina | deaths | 333 | 2020-11-28 | 0.8 | 0.9 | 1.0 |
| Tunisia | deaths | 422 | 2020-11-28 | 0.8 | 0.9 | 1.0 |
| Czechia | deaths | 946 | 2020-11-28 | 0.9 | 0.9 | 1.0 |
| Country | Estimated Type | Count (Last Week) | Week Ending | R - Lower CI | R - Mean | R - Uppper CI |
|---|---|---|---|---|---|---|
| Oman | cases | 1,219 | 2020-11-28 | 0.5 | 0.6 | 0.6 |
| Belgium | cases | 11,878 | 2020-11-28 | 0.6 | 0.6 | 0.6 |
| France | cases | 87,029 | 2020-11-28 | 0.6 | 0.6 | 0.6 |
| Somalia | cases | 63 | 2020-11-28 | 0.5 | 0.6 | 0.8 |
| Ghana | cases | 594 | 2020-11-28 | 0.6 | 0.7 | 0.8 |
| Zambia | cases | 196 | 2020-11-28 | 0.6 | 0.7 | 0.8 |
| Ireland | cases | 1,897 | 2020-11-28 | 0.7 | 0.8 | 0.8 |
| Kuwait | cases | 2,568 | 2020-11-28 | 0.7 | 0.8 | 0.8 |
| Uzbekistan | cases | 1,129 | 2020-11-28 | 0.8 | 0.8 | 0.8 |
| United_Kingdom | cases | 115,793 | 2020-11-28 | 0.8 | 0.8 | 0.8 |
| Country | Estimated Type | Count (Last Week) | Week Ending | R - Lower CI | R - Mean | R - Uppper CI |
|---|---|---|---|---|---|---|
| Honduras | deaths | 60 | 2020-11-28 | 1.2 | 1.6 | 2.0 |
| Slovenia | deaths | 239 | 2020-11-28 | 1.3 | 1.5 | 1.7 |
| Serbia | deaths | 283 | 2020-11-28 | 1.3 | 1.5 | 1.7 |
| Israel | deaths | 95 | 2020-11-28 | 1.1 | 1.4 | 1.8 |
| Ecuador | deaths | 263 | 2020-11-28 | 1.2 | 1.4 | 1.6 |
| Nepal | deaths | 137 | 2020-11-28 | 1.2 | 1.4 | 1.6 |
| Japan | deaths | 111 | 2020-11-28 | 1.1 | 1.3 | 1.6 |
| Greece | deaths | 683 | 2020-11-28 | 1.2 | 1.3 | 1.5 |
| Germany | deaths | 2,081 | 2020-11-28 | 1.3 | 1.3 | 1.4 |
| Albania | deaths | 99 | 2020-11-28 | 1.1 | 1.3 | 1.6 |
| Country | Estimated Type | Count (Last Week) | Week Ending | R - Lower CI | R - Mean | R - Uppper CI |
|---|---|---|---|---|---|---|
| Yemen | cases | 58 | 2020-11-28 | 1.6 | 2.2 | 2.9 |
| Niger | cases | 132 | 2020-11-28 | 1.6 | 1.9 | 2.3 |
| Nicaragua | cases | 123 | 2020-11-28 | 1.3 | 1.8 | 2.5 |
| Mauritania | cases | 392 | 2020-11-28 | 1.6 | 1.8 | 2.0 |
| Honduras | cases | 3,646 | 2020-11-28 | 1.6 | 1.7 | 1.8 |
| Thailand | cases | 64 | 2020-11-28 | 1.3 | 1.7 | 2.1 |
| South_Sudan | cases | 76 | 2020-11-28 | 1.2 | 1.6 | 2.0 |
| Eswatini | cases | 177 | 2020-11-28 | 1.4 | 1.6 | 1.8 |
| Mali | cases | 474 | 2020-11-28 | 1.4 | 1.5 | 1.7 |
| Zimbabwe | cases | 594 | 2020-11-28 | 1.3 | 1.5 | 1.6 |
Below we plot results for each country/province in a list. We filter out weeks where the upper end of confidence interval for \(R_{t,m}\) exceeds five.
## Detailed Output
Detailed output for all countries are saved to a comma-separated value file. The file can be found here.
Limitation of this method to estimate \(R_{t,m}\) are noted in [1]
Further to the above the estimates are made under assumption that the cases and deaths are reported consistently over time. For cases this means that testing needs to be at similar levels and reported with similar lag. Should these change rapidly over an interval of a few weeks the above estimates of the effective reproduction numbers would be biased. For example a rapid expansion of testing over the last 3 weeks would results in overestimating recent effective reproduction numbers. Similarly any changes in reporting (over time and underreporting) of deaths would also bias estimates of the reproduction number estimated using deaths.
Estimates for the reproduction number are plotted in time period in which the relevant measure is recorded. Though in reality the infections giving rise to those estimates would have occurred roughly between a week to 4 weeks earlier depending on whether it was cases or deaths. These figures have not been shifted back.
Despite these limitation we believe the ease of calculation of this method and the ability to use multiple sources makes it useful as a monitoring tool.
[1] A. Cori, N. M. Ferguson, C. Fraser, and S. Cauchemez, “A new framework and software to estimate time-varying reproduction numbers during epidemics,” American Journal of Epidemiology, vol. 178, no. 9, pp. 1505–1512, Sep. 2013, doi: 10.1093/aje/kwt133. [Online]. Available: https://doi.org/10.1093/aje/kwt133
[2] A. Cori, EpiEstim: A package to estimate time varying reproduction numbers from epidemic curves. 2013 [Online]. Available: https://CRAN.R-project.org/package=EpiEstim
[3] European Centre for Disease Prevention and Control, “Data on the geographic distribution of COVID-19 cases worldwide.” European Union, 2020 [Online]. Available: https://www.ecdc.europa.eu/en/publications-data/download-todays-data-geographic-distribution-covid-19-cases-worldwide